Rational actors should never adopt strategies that are “dominated” by other strategies

A strategy is weakly dominant if, when you compare it to another strategy, it yields a better outcome in at least one respect and is as good or better than the other strategy in all other respects (where “better” means that it leads to an outcome with greater utility).

A strategy is strongly dominant if, when compared to another, it yields an outcome superior in every aspect

What is the ordering of alternatives axiom?

Rational decision makers should be able to compare any two alternatives.

They should either prefer one alternative to the other, or they should be indifferent to them.

What is the cancellation axiom?

If two risky alternatives include identical and equally probable outcomes among their possible consequences, then the utility of these outcomes should be ignored in choosing between the two options.

A choice between two alternatives should depend only on those outcomes that differ, not on outcomes that are the same for both alternatives.

Common factors should cancel out.

What is the transitivity axiom?

If a rational decision maker prefers Outcome A to Outcome B, and Outcome B to Outcome C, then that person should prefer Outcome A to Outcome C.

What is the continuity axiom?

For any set of outcomes, a decision maker should always prefer a gamble between the best and worst outcomes to a sure intermediate outcome if the odds of the best outcome are good enough.

What is the invariance axiom?

A decision maker should not be affected by the way alternatives are presented.

I.e there should be no preference between a two stage lottery with a 50% chance of winning £100 or a simple one stage gamble with a 25% chance of winning £100